A100150 Structured snub cubic numbers.

1, 24, 107, 288, 605, 1096, 1799, 2752, 3993, 5560, 7491, 9824, 12597, 15848, 19615, 23936, 28849, 34392, 40603, 47520, 55181, 63624, 72887, 83008, 94025, 105976, 118899, 132832, 147813, 163880, 181071, 199424, 218977, 239768, 261835, 285216, 309949, 336072

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100149, A100151 for adjacent structured Archimedean solids; and A100145 for more on structured polyhedral numbers.

Programs

Magma

[(1/6)*(38*n^3-48*n^2+16*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,24,107,288},40] (* Harvey P. Dale, Sep 17 2020 *)

PARI

a(n)=n*(38*n^2-48*n+16)/6 \\ Charles R Greathouse IV, Jul 18 2011

Formula

a(n) = (1/6)*(38*n^3 - 48*n^2 + 16*n).

G.f.: x*(1 + 20*x + 17*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

From Elmo R. Oliveira, Aug 05 2025: (Start)

E.g.f.: exp(x)*x*(19*x^2 + 33*x + 3)/3.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

Extensions

Deleted extra +16 in formula, corrected by Craig Ferguson, Jul 18 2011